{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HSROHUWOWX6CAPGNETVVOVIRCH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e73e89fb120bf2323592ef7651e30ecfb6f87711003ee44dfbda7237c56bad0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-23T11:52:49Z","title_canon_sha256":"7c678a5a86ec081c03014de73252121058fc6f8f1ebd4c88202497b661d17c2f"},"schema_version":"1.0","source":{"id":"1412.7330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7330","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7330v2","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7330","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"pith_short_12","alias_value":"HSROHUWOWX6C","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HSROHUWOWX6CAPGN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HSROHUWO","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b765a935a9e3821a98bfbed93ff87a359f9617c7660eba52878d77a538beb92d","target":"graph","created_at":"2026-05-18T01:22:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |N_G(H):H| is finite for every non-normal subgroup H of G, and (ii) |C_G(x):<x>| is finite for every non-normal cyclic subgroup <x> of G. We show that (i) and (ii) are equivalent in the classes of locally finite groups and locally nilpotent groups. In both cases, the groups satisfying these conditions are a special kind of cyclic extensions of Dedekind groups. We also study a variation of (i) and (ii), where the requirement of finiteness is replaced with a bound. In this setting, we extend our","authors_text":"Antonio Tortora, Gustavo A. Fernandez-Alcober, Leire Legarreta, Maria Tota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-23T11:52:49Z","title":"Some finiteness conditions on normalizers or centralizers in groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7330","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d68c1bb025eea21187b4c1bda8da33335414fb46ae0b4d78e6aa88a2cf7921d","target":"record","created_at":"2026-05-18T01:22:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e73e89fb120bf2323592ef7651e30ecfb6f87711003ee44dfbda7237c56bad0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-23T11:52:49Z","title_canon_sha256":"7c678a5a86ec081c03014de73252121058fc6f8f1ebd4c88202497b661d17c2f"},"schema_version":"1.0","source":{"id":"1412.7330","kind":"arxiv","version":2}},"canonical_sha256":"3ca2e3d2ceb5fc203ccd24eb57551111fc5fba28cc2b11281731a53070cebd0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ca2e3d2ceb5fc203ccd24eb57551111fc5fba28cc2b11281731a53070cebd0c","first_computed_at":"2026-05-18T01:22:57.861680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:57.861680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DD64rKo4nsK99YuQlmPys7yNFl3UAwT8owLqxT06rDhyi2TQijq2bgRqleJO8HG48iUKfFMQc5cLkiSdO66BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:57.862251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d68c1bb025eea21187b4c1bda8da33335414fb46ae0b4d78e6aa88a2cf7921d","sha256:b765a935a9e3821a98bfbed93ff87a359f9617c7660eba52878d77a538beb92d"],"state_sha256":"2be9324cc4bb9857a0bcd9a7313b2b23ac101f9791094661889ca33284772e84"}